Entropy as a Complexity effect in Innovation

What is it about?

This paper offers novel insights regarding the role of complexity in both the transitional and the long-run dynamics of the economy. We devise an endogenous growth model that encompasses long-run economic change building on the concept of entropy as a time- varying state-dependent complexity effect. We show that the empirical evidence supports entropy as an ’operator’ of the complexity effect. It also suggests that part of the modern innovations have a stabilizing role in the complexity of the economies, as the ‘operator’ levels off despite the continuous increase in the measure of technological varieties. The model features endogenous growth, with null or small scale effects, or stagnation, in the long run. The model can replicate well the take-off after the industrial revolution and the productivity slowdown in the second half of the XXth century. Long-run scenarios based on in-sample calibration are discussed, and may help explain (part of) the growth crises affecting the current generation.

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Why is it important?

Overall, our model produces novel insights regarding the role of complexity in the economy. Firstly, our model generates a non-monotonic U-inverted transition of the TFP growth rate commanded by the complexity index dynamics irrespective of the dynamics of the physical inputs. Secondly, the estimation of the complexity (entropy) index based on historical data suggests an eventual stabilization of complexity as time goes by (which is shown to be related to the notion of entropy and of sub-extensive system). This speaks to the fact that, in practice, new ideas and new varieties of technological goods seem to have a heterogeneous impact on complexity, with some increasing it but others producing a stabilizing effect, and suggests, as a macro-behavioral interpretation, that there is a relatively high level of complementarity of ideas (or, alternatively, a relatively high ’relative risk aversion’ to adopt new ideas) in the modern knowledge system. Finally, the model shows that it is not a necessary condition to have ever-increasing complexity as the stock of knowledge and of varieties of technological goods increase in order to generate permanent lower growth of TFP or even stagnation as a long-run equilibrium. Instead, the key feature is the level at which complexity stabilizes and thereby to what extent it curtails scale effects on growth.

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